Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:292AM GHM

Order: 20

Horizontal side: 292 Vertical side: 292

Elements: 3, 3√2, 6, 9, 10, 12, 10√2, 15√2, 22, 21√2, 42, 52, 52√2, 94, 104, 94√2, 146, 104√2, 188, 146√2.

Code: 1885 0 104 1464 146 146 1463 292 146 421 188 146 212 209 125 524 240 94 523 292 94 63 209 119 95 209 116 150 203 119 34 206 116 33 209 116 121 218 116 225 218 94 1045 0 0 1044 104 0 100 208 104 101 218 104 940 198 94 941 292 94

The properties below may precede order:side in a tiling's title:

• c = crossed. There is a tile-corner traversed by two lines. The only known crossed PPIRTS's below order 20 are 19:35AB1of4 and 19:35AB4of4.
• d = double-pentagon patterned. Every such tiling is a subdivision of an instance of the same deformable tiling by two 45-90-90-90-225 pentagons with a shared side, four triangles and two pseudotriangles. All below order 19 are degenerate in the sense that one or more sides of underlying tiles have shrunk to zero length. The non-degenerate d-tilings of order 19 are 19:221AA, 19:229AB and 19:241AA.
• e = elegant. No tile-corner is just a T-junction. Such tilings may be considered aesthetically pleasing. The only known elegant PPIRTS's below order 16 are 13:21AA, 14:26AJ, 14:35AA and 15:55AA.
• i = isomers exist which are ineligible for this catalogue. They are not included in the isomer count which follows 'of' in the tiling id.
• r = rectangular inclusion. The only known PPIRTS's below order 16 with a rectangular inclusion are 13:18AA1-4of4 and 15:44AA1-4of4.

Credit for Discovery

Just three people are credited with the discovery of Primitive Perfects:

Geoffrey H. Morley (GHM, England)

Jasper D. Skinner, II (JDS, United States)

William T. Tutte (WTT, Canada, 1917-2002) (15:44AI, 17:136AJ and 19:56AJ only)